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arXiv · 2201.11061

Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory

Jean Alexandre·John Ellis·Peter Millington
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Abstract

We extend to a non-Hermitian fermionic quantum field theory with PT symmetry our previous discussion of second quantization, discrete symmetry transformations, and inner products in a scalar field theory [arXiv:2006.06656]. For illustration, we consider a prototype model containing a single Dirac fermion with a parity-odd, anti-Hermitian mass term. In the phase of unbroken PT symmetry, this Dirac fermion model is equivalent to a Hermitian theory under a similarity transformation, with the non-Hermitian nature of the model residing only in the spinor structure, whereas the algebra of the creation and annihilation operators is just that of a Hermitian theory.

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Jean Alexandre, John Ellis, Peter Millington. 2022-09-09. Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory. https://doi.org/10.1103/physrevd.106.065003

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